Broadband spectroscopic rotating compensator ellipsometer

ABSTRACT

An ellipsometer, and a method of ellipsometry, for analyzing a sample using a broad range of wavelengths, includes a light source for generating a beam of polychromatic light having a range of wavelengths of light for interacting with the sample. A polarizer polarizes the light beam before the light beam interacts with the sample. A rotating compensator induces phase retardations of a polarization state of the light beam wherein the range of wavelengths and the compensator are selected such that at least a first phase retardation value is induced that is within a primary range of effective retardations of substantially 135° to 225°, and at least a second phase retardation value is induced that is outside of the primary range. An analyzer interacts with the light beam after the light beam interacts with the sample. A detector measures the intensity of light after interacting with the analyzer as a function of compensator angle and of wavelength, preferably at all wavelengths simultaneously. A processor determines the polarization state of the beam as it impinges the analyzer from the light intensities measured by the detector.

FIELD OF THE INVENTION

[0001] The present invention relates to ellipsometers, and moreparticularly to rotating compensator ellipsometers.

BACKGROUND OF THE INVENTION

[0002] Optical ellipsometry has long been recognized as providingaccurate characterizations of semiconductors and other materials, theirsurface conditions, layer compositions and thicknesses, and forcharacterizing overlying oxide layers. This non-destructive technique isparticularly needed to evaluate thickness, crystallinity, compositionand index of refraction characteristics of thin films deposited onsemiconductor or metal substrates to ensure high yields duringfabrication.

[0003] An ellipsometer probes a sample with a light beam having a knownpolarization state. The light beam is reflected at a non-normalincidence from the surface of the sample. The polarization state of thebeam is, modified upon reflection in a way that depends upon thestructure of the sample. By accurately measuring the polarization stateof the reflected beam and comparing it to the original polarizationstate, various properties of the sample can be ascertained.

[0004] In spectroscopic ellipsometry, the probing wavelength is changedand the ellipsometric measurement is repeated at each new wavelength.Spectroscopic ellipsometry is ideal for multi-material samples formed instacked layers. The different depth penetrations and spectral responsesthat vary depending upon the material and wavelength of light provideadditional information about a sample that is not available using singlewavelength ellipsometers.

[0005] One possible ellipsometric configuration uses the followingcomponents: 1) a light source, 2) a linear polarizer (“polarizer”), 3)the sample (to be analyzed), 4) a second linear polarizer (“analyzer”),and 5) a detector. The polarizer produces totally polarized light, andthe analyzer assesses the polarization state of the beam afterreflection from the sample. Either the polarizer or the analyzer isrotated so that the detector signal can be used to accurately measurethe linear polarization component of the reflected beam. Then, thecircularly polarized component is inferred by assuming that the beam istotally polarized, and what isn't linearly polarized must be circularlypolarized.

[0006] An advantage of this type of ellipsometer is that the polarizerand analyzer can function over a wide range of wavelengths, thusproviding a broad perspective of the sample as compared to measurementsmade at a single wavelength. A common method of spectroscopicellipsometry is to use a broadband light source, such as a Xe arc lamp,with data acquisition occurring in a serial or parallel mode. In theserial mode, a monochrometer is placed before the detector to filter outall wavelengths except for the desired probe wavelength.Multi-wavelength measurements are performed serially, one wavelength ata time, by properly adjusting the monochrometer for each measurement. Inparallel operation, a polychromatic light beam having a broad range ofwavelengths is directed to the sample. The reflected beam is diffractedto a photodetector array or an optical multichannel analyzer by adiffraction grating or a prism. The multi-wavelength measurements areperformed in parallel, with all wavelengths of interest being measuredat the same time.

[0007] Such an ellipsometer, commonly called a rotating-polarizer orrotating-analyzer ellipsometer, is termed “an incomplete” polarimeter,because it is insensitive to the handedness of the circularly polarizedcomponent and exhibits poor performance when the light being analyzed iseither nearly completely linearly polarized or possesses a depolarizedcomponent.

[0008] The latter limitations of the rotating-polarizer androtating-analyzer ellipsometers can be overcome by including a rotatingcompensator placed between the polarizer and the analyzer (both of whichare fixed and not rotating) that rotates about the propagating axis ofthe beam. The compensator can be placed either between the sample andthe polarizer, or between the sample and the analyzer. Such aconfiguration is commonly called a rotating compensator ellipsometer.The compensator is an optical component that delays the light polarizedparallel to its slow axis relative to light polarized parallel to itsfast axis by an amount proportional to the refractive index differencealong the two directions and the thickness of the plate, and inverselyproportional to the wavelength of the light.

[0009] It is known in the art that the intensity I of a beam transmittedthrough an ideal compensator-analyzer combination is expressed as:

I[|E _(x)|² +|E _(y)|² ]=I _(o) [|E _(x)|²(cos²(δ

[0010] /2)+(½)sin²(δ/2))+|E _(y)|²(½)sin²(δ/2)+(|E _(x)|² −|E_(y)|²)(½)sin²(δ/2)cos(4C)+Re(E _(x) E _(y)*)sin²(δ/2)sin(4C)−Im(E _(x)E _(y)*)sinδ sin(2C)],  (1)

[0011] where I_(o) is the intensity of the incoming beam, E_(x) andE_(y) are the projections of the incident electric field vector paralleland perpendicular, respectively, to the transmission axis of theanalyzer, δ is the phase retardation of the compensator, C is theazimuth (rotational) angle of the fast (reference) axis of thecompensator also relative to the transmission axis of the analyzer. Inthe case of a continuously rotating compensator, C=ωt, where ω is theangular rotational frequency of the compensator.

[0012] As can be seen by Eqn. (1), a rotating compensator will generatea signal having a dc component, a 2ω (two omega) component and a 4ω(four omega) component with respect to the rotation rate of thecompensator. While usable information is generated from both the twoomega and four omega signals, it is often felt that the two omega signalis the most significant for analysis. The two omega component ismaximized when the phase retardation of the compensator is 90° (i.e. sinδ=1), and disappears at phase retardations of 0° and 180° (sin δ=0).Since the phase retardation of the compensator is a function ofwavelength, this system lends itself to single wavelength operationonly, or to a range where the wavelength changes only by a relativelysmall amount from the center wavelength of the compensator. As thewavelength deviates from the center wavelength such that the amount ofphase retardation induced by the compensator deviates from 90 degrees,the relative intensity of the two omega signal is reduced. Therefore,multiple wavelength operation of rotating compensator ellipsometers hastraditionally been limited to relatively narrow wavelength ranges (lessthan a factor of two in wavelength) corresponding to substantially 90degree phase retardations induced by the compensator.

[0013] There is a need for a rotating compensator ellipsometer systemthat simultaneously obtains data over a wide range of wavelengths, whichnecessarily corresponds to phase retardations that vary significantlyfrom the optimal 90°.

[0014] One prior-art solution to expand the effective wavelength rangeof retardation-based ellipsometers is to replace the rotatingcompensator with a photoelastic modulator. The phase retardation of thephotoelastic modulator is a function of both the wavelength and thedrive voltage to the modulator. During ellipsometric measurements, aseries of wavelengths within the wavelength range of interest aresequentially scanned while the drive voltage to the photoelasticmodulator is simultaneously changed. The change in drive voltage tracksthe change in wavelength such that the phase retardation of themodulator is maintained at approximately 90° when each wavelength ismeasured to maximize the two omega signal. The drawback of such aspectroscopic ellipsometer is that the wavelengths are scannedsequentially, and not in parallel, which results in a reducedsignal-to-noise ratio for the same scan time. Also, such modulatorsoperate at frequencies (for example 50 KHz) that are too high forphotodiode array detectors to follow.

[0015] Another prior-art solution is to use a quasiachromatic wave platefor which the retardation is relatively invariant for a finitewavelength range. Such plates, often called Pancharatnam plates, arecommonly used in astronomy as reviewed by K. Serkowski in the compendiumPlanets, Stars, and Nebulae studied with Photopolarimetry, ed. T.Gehrels (University of Arizona Press, Tucson, 1974), pp. 135-174. Onepolarimeter of a half-wave design is discussed in a paper by D. Clarkeand R. N. Ibbett, J. Sci. Inst. Series 2, 1, 409-412 (1968), who used afixed mica half-wave plate to test a concept but warned on p. 410 that“A simple half-wave plate is useful over a range of about 300 Å. Forextended wavelength ranges an achromatic half-wave plate must beconsidered.”

[0016] Numerous configurations involving quarter-wave and half-waveretarders, in some cases combined to form quasiachromatic quarter- andhalf-wave plates, have been reviewed by Serkowski in the above mentionedvolume. Other discussions can be found in the book Polarized Light andOptical Measurement by. D. Clarke and J. F. Grainger (Pergamon, Oxford,1971). In the configurations listed, the quarter-wave plates are usedfor quarter-wave retardation and the half-wave plates for half-waveretardation. As discussed in the article by Serkowski, it is possible tocombine retarders that exhibit quarter- and half-wavelength retardationat a specific wavelength to achieve quasiachromatic quarter- orhalf-wavelength retardation behavior over a range of wavelengthsHowever, the usable range for a triple (Pancharatnam) stack of suchplates does not exceed a factor of 2, and a 6-fold (Serkowski) stack ofsuch plates does not exceed a factor of about 3. Further, these stacksare intrinsically complex and very difficult to align (and to maintainsuch alignment). In addition, the azimuth angles of the principle axesof these stacks are not fixed with respect to the elements but vary withwavelength. None of these references contemplate a wide-bandwidthinstrument using a single quarter-wave retarder over a wide range ofwavelengths that includes half-wave retardation.

[0017] There is a need for a spectroscopic ellipsometer that operateswith parallel detection over a relatively broad wavelength range (on theorder of at least a factor of four) such that useful information can besimultaneously obtained throughout the entire wavelength range.

SUMMARY OF THE INVENTION

[0018] It has been discovered by the present inventors that a sample canbe analyzed with good accuracy if information obtained from both the twoomega and four omega components of the rotating compensatorspectroscopic ellipsometer signal are combined. In particular, thisallows spectroscopic ellipsometric analysis to be performed over verylarge ranges of wavelengths, as long as both the two omega and fouromega signals are utilized and at least one of the signals is present atevery wavelength measured. The broadband spectroscopic ellipsometer ofthe present invention simultaneously measures at wavelengths of lightwithin a broad wavelength range of interest, where the measurementwavelengths measured correspond to compensator phase retardations thatare sufficiently near 180° and sufficiently near at least 90° or 270°.

[0019] The ellipsometer of the present invention includes a lightgenerator that generates a beam of polychromatic light having a range ofwavelengths and a known polarization for interacting with the sample. Acompensator is disposed in the path of the light beam to induce phaseretardations of the polarization state of the light beam. The range ofwavelengths and the compensator are selected such that at least a firsteffective phase retardation value is induced that is within a primaryrange of effective retardations of substantially 135° to 225°, and atleast a second effective phase retardation value is induced that isoutside of that primary range. The compensator is rotatable about anaxis substantially parallel to the propagation direction of the lightbeam. An analyzer interacts with the light beam after the light beaminteracts with the sample. A detector measures intensity of the lightafter the interaction with the analyzer as a function of the rotationalangle of the compensator and of wavelength, including light intensitiesof those wavelengths corresponding to the first and second effectivephase retardation values. These intensities can be analyzed for thepolarization state of the light incident on the analyzer.

[0020] The method of analyzing a sample using the ellipsometer of thepresent invention includes generating a beam of polychromatic lighthaving a range of wavelengths and a known polarization for interactingwith the sample. Phase retardations of a polarization state of the lightbeam are induced with a compensator by selecting the range ofwavelengths and the compensator such that at least a first effectivephase retardation value is induced that is within a primary range ofeffective phase retardations of substantially 135° to 225°, and at leasta second effective phase retardation value is induced that is outside ofthat primary range. The compensator is rotated about an axissubstantially parallel to the propagation direction of the light beam.The light beam is subjected to interaction with an analyzer after thebeam interacts with the sample. The intensity of the light is measuredafter the interaction with the analyzer as a function of the rotationalangle of the compensator and of wavelength, including light intensitiesof those wavelengths corresponding to the first and second effectivephase retardation values. These intensities correspond to thepolarization state of the light impinging on the analyzer.

[0021] Other aspects and features of the present invention will becomeapparent by a review of the specification, claims and appended figures.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022]FIG. 1 is a plan view of the ellipsometer of the presentinvention.

[0023]FIG. 2 is a plan view of a multiple wavelength detector used withthe present invention.

[0024]FIG. 3 is a graph illustrating the sensitivities of thesensitivity coefficients involving ψ′ and Δ′ as a function ofcompensator retardation.

[0025]FIG. 4 is a plan view of an alternate embodiment of theellipsometer of the present invention.

[0026]FIG. 5 is a plan view of a multiple wavelength detector used withthe alternate embodiment of the present invention.

[0027]FIG. 6 is a plan view of a second embodiment of a multiplewavelength detector used with the alternate embodiment of theellipsometer of the present invention.

[0028]FIG. 7. is an illustration depicting the appearance of probe beamsassociated with two different wavelengths after the probe beam haspassed through the dispersion element of FIG. 6.

[0029]FIG. 8. is a third embodiment of the multi-wavelength detectorused with the alternate embodiment of the ellipsometer of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] The present invention is a broadband rotating-compensatorspectroscopic ellipsometer that simultaneously measures the polarizationstates of a broad range of wavelengths contained in a probe beamreflected from a test sample. The preferred embodiment is illustrated inFIG. 1. The ellipsometer 1, for probing a sample 2, includes a,broadband light source 4, a polarizer 6, a rotating compensator 8, ananalyzer 10 and a detector 12.

[0031] The light source 4 is a broadband light source that produces aspectrum of polychromatic light over a predetermined wavelength range ofinterest. For example, when analyzing semiconductors, one possiblepredetermined wavelength range of interest would be 200 to 800 nm. Thepreferred embodiment uses a high pressure Xe arc lamp to produce abroadband light beam 14 having wavelengths throughout the 200-800 nmwavelength range of interest. The diverging beam 14 from the lightsource 4 is collimated by a lens 16, such as an achromatic lens, oralternately a focusing mirror.

[0032] The beam 14 interacts with polarizer 6 to create a knownpolarization state. In the preferred embodiment, polarizer 6 is a linearpolarizer made from a quartz Rochon prism, but in general thepolarization does not necessarily have to be linear, nor even complete.Polarizer 6 can also be made from calcite, for systems operating atwavelengths longer than 230 nm, or magnesium fluoride, for systemsoperating at wavelengths shorter than 200 nm. The azimuth angle ofpolarizer 6 is oriented so that the plane of the electric vectorassociated with the linearly polarized beam exiting from the polarizer 6is at a known angle with respect to the plane of incidence (defined bythe propagation direction of the beam 14 and the normal N to the exposedsurface of the sample 2). The azimuth angle is preferably selected to beon the order of 30° because the sensitivity is optimized when thereflected intensities of the P and S polarized components areapproximately balanced. It should be noted that polarizer 6 can beomitted if a particular light source is used that emits light with thedesired known polarization state.

[0033] The beam 14 is incident on, and reflects from, sample 2 at anoblique angle. For this discussion, sample 2 consists of a thin layer 3formed on a substrate 5, however in general the sample can be bare ormultiple thin layers 3 can exist one on top of the other. The usefullight is the light reflected by the sample 2 symmetrically to theincident beam about the normal N to the surface of the sample 2,although we note that the polarization state of nonspecularly scatteredradiation can be determined by the method of the present invention aswell. The beam 14 is ideally incident on sample 2 at an angle on theorder of 70° to the normal N of the surface of the sample becausesensitivity to sample properties is maximized in the vicinity of theBrewster or pseudo-Brewster angle of a material. Based upon well knownellipsometric principles, the reflected beam will generally have a mixedlinear and circular polarization state after interacting with thesample, as compared to the linear polarization state of the incomingbeam.

[0034] The beam 14 then passes through the rotating compensator 8, whichintroduces a relative phase delay δ (phase retardation) between a pairof mutually orthogonal polarized optical beam components. The amount ofphase retardation is a function of the wavelength, the dispersioncharacteristics of the material used to form the compensator, and thethickness of the compensator. Compensator 8 is rotated at an angularvelocity ω about an axis substantially parallel to the propagationdirection of beam 14, preferably by an electric motor 9. Compensator 8can be any conventional wave-plate compensator, for example those madeof crystal quartz. The thickness and material of the compensator 8 isselected such that a desired range of phase retardations of the beam isinduced by the range of wavelengths used to probe the sample. In thepreferred embodiment, compensator 8 is a bi-plate compensatorconstructed of two parallel plates of anisotropic (usually birefringent)material, such as quartz crystals of opposite handedness, where the fastaxes of the two plates are perpendicular to each other and thethicknesses are nearly equal, differing only by enough to realize a netfirst-order retardation over the wavelength range of interest.

[0035] Beam 14 then interacts with analyzer 10, which serves to mix thepolarization states incident on it. In this embodiment, analyzer 10 isanother linear polarizer, preferably oriented at an azimuth angle of 45°relative to the plane of incidence. However, any optical device thatserves to appropriately mix the incoming polarization states can be usedas an analyzer. The analyzer 10 is preferably a quartz Rochon orWollaston prism. The rotating compensator changes the polarization stateof the beam as it rotates such that the light transmitted by analyzer 10is characterized by Eqn. (1) discussed above. By measuring the lighttransmitted by analyzer 10, the polarization state of beam 14 reflectedfrom the sample can be determined.

[0036] It should be noted that the compensator 8 can be located eitherbetween the sample 2 and the analyzer 10 (as shown in FIG. 1), orbetween the sample 2 and the polarizer 6. Further, the polarizers couldbe reflection polarizers in a vacuum for ultraviolet wavelengths.

[0037] Beam 14 then enters detector 12, which measures the intensity ofthe different wavelengths of light throughout the wavelength range ofinterest that pass through the compensator/analyzer combination.Detector 12 ideally includes a dispersive element 18, such as adiffraction grating, prism or holographic plate, to angularly dispersethe beam 14 as a function of wavelength to individual detector elements20 contained in a detector array 22, as illustrated in FIG. 2 (with adiffraction grating). The different detector elements 20 measure theoptical intensities of the different wavelengths of light throughout thewavelength range of interest, preferably simultaneously. Alternately,detector 12 can be a CCD camera, or a photomultiplier with suitablydispersive or otherwise wavelength selective optics. It should be notedthat it is within the scope of this invention to use a monochrometer,etc., and measure the different wavelengths serially (one wavelength ata time) using a single detector element.

[0038] A processor 23 processes the intensity information measured bythe detector 12 to determine the polarization state of the light afterinteracting with the analyzer, and the ellipsometric parameters of thesample. This information processing not only includes measuring beamintensity as a function of wavelength, but also measuring beam intensityas a function of the azimuth (rotational) angle of the compensator aboutits axis of rotation (which is substantially parallel to the propagationdirection of beam 14). This measurement of intensity as a function ofcompensator rotational angle is effectively a measurement of theintensity of beam 14 as a function of time, since the compensatorangular velocity is usually known and a constant.

[0039] The rotating compensator ellipsometer is ideal for analyzingsamples with probe beams having such a large range of wavelengths thatthe range of phase retardations induced by the compensator includesretardation values at or near 90° (and/or 270°) and at or near 180°,including any multiple of ±360° (as illustrated in FIG. 3 discussedbelow). The range of phase retardations is dictated by the compensatorthickness and material, as well as the range of wavelengths selected toprobe the sample. For example, when the ellipsometer of the presentinvention is used to analyze. semiconductor materials and structures,where the wavelength range of interest is 200 nm to 800 nm, thethicknesses of the dual quartz plates of the compensator 8. are about 1mm each with a thickness difference of about 12.6 μm so as to imposeupon beam 14 a range of phase retardations of about 50° to 300° as thewavelength varies from 200 nm to 800 nm. For any given wavelength withinthe 600 nm range, either the two omega signal, or the four omega signal,or both signals, supply information about the sample.

[0040] It has been discovered that useful information can be derivedfrom the above spectroscopic ellipsometer even though some Fouriercomponents may exhibit low sensitivity or even vanish somewhere withinthis broad spectral range. This enables the ellipsometer of the presentinvention to simultaneously measure and provide useful information aboutthe sample over a very broad range of wavelengths.

[0041] A method of determining the polarization state and therefore thephysical parameters of the thin film 3 using the above ellipsometer willnow be explained.

[0042] For the following discussion it is convenient to recast Eqn. (1)in terms of normalized Fourier coefficients β₂, α₄, and β₄ defined as

I=I _(o)[1+β₂ sin 2ωt+α ₄ cos 4ωt+β ₄ sin 4ωt],  (2)

[0043] since these are the coefficients that are determinedexperimentally, e.g., by a harmonic analysis of the detectedphotoelectric current. We assume that an electric field E is incident onthe rotating compensator. One can represent the electric field in termsof components E_(x) and E_(y), where E_(x) and E_(y) are the projectionsof E onto the coordinate axes x and y defined by the fixed analyzer,where in the absence of the compensator the analyzer would pass thecomponent polarized along x and block that polarized along y. Since onlyrelative intensities matter, it is useful to define a relative amplitudetan ψ′ and a relative phase Δ′ for the two components such that tanψ′exp(iΔ′)=E_(y)/E_(x). In the presence of the rotating compensator, theintensity transmitted through the rotating-compensator/analyzercombination can be represented by relating the normalized coefficientsto tan ψ′ and cos Δ′. This connection is given by:

β₂=[sin Δ′ sin δ sin 2ψ′]/D;  (3a)

α₄=[sin²(δ/2)cos 2ψ′]/D;  (3b)

β₄=[cos Δ′sin²(δ/2)sin 2ψ′]/D;  (3c)

where

D=[1+cos²(δ/2)]cos²ψ′+sin²(δ/2)sin²ψ′.  (3d)

[0044] For purposes of discussing the capabilities of the ellipsometerof the present invention over a wide spectral range (wide range ofretardations δ) we now define the following sensitivity coefficients:∂β₂/∂ψ′, ∂β₂/∂Δ′, ∂β₂/∂δ, ∂α₄/∂ψ′, ∂α₄/∂Δ′, ∂α₄/∂δ, ∂β₄/∂ψ′, ∂β₄/∂Δ′,∂β₄/∂δ. These can be calculated directly from Eqns. (3a) to (3d) above,and represent physically the influence of the several parameters on theseveral normalized coefficients. For example,

∂β₄/∂Δ′=−[sin Δ′ sin²(δ/2)sin 2ψ′]/D.  (4)

[0045] The importance of the sensitivity coefficient is that the largera given sensitivity coefficient is, the stronger the connection betweenthat particular normalized Fourier coefficient and the variable inquestion.

[0046] As an example of the above procedure, we consider a dielectricmaterial appropriate to silicon for wavelengths longer than about 370nm. We suppose that the incident beam is linearly polarized, with themajor axis of its polarization azimuth oriented along 45°. The resultsof a sensitivity calculation for this case is shown in FIG. 3. Here, thesensitivity coefficients involving ψ′ and Δ′ are plotted for the entirerange of relative retardations 0 to 90° for Δ′ and for the entire 0 to360° retardation range of the compensator retardation δ.

[0047] We note that broadband spectral ellipsometric operation at anyactual retardation value, i.e. X°, is effectively equivalent tooperation at retardation values at multiples of 360°, i.e. X°±n360°,where n is any integer. Similarly, any actual phase retardation range,such as X° to Y°, is effectively equivalent to operation at any rangeX°+n360° to Y°+n360°. Therefore, for the purposes of this disclosure andappending claims, it should be assumed that any discussion regarding anactual phase retardation value (or an actual range of values)effectively applies to the corresponding “effective” retardation value(or range of values), which are the plus or minus 360° multiples of theactual retardation values (ranges). Alternately, any “effective”retardation value (or range) encompasses the actual value (or range) andany 360° multiple thereof.

[0048] It is clear that information is available over virtually theentire range of retardations from 0° to 360°, and broadband operation ofthe ellipsometer described above throughout much of this 360°retardation range would provide exceptional information on the samplebeing probed. The information is carried by different coefficients indifferent ranges. For example, FIG. 3 illustrates three compensationangle ranges: range I from about 0° to 135°, range II from about 135° to225°, and range III from about 225° to 360°. As illustrated by FIG. 3,the sensitivity to ψ′ occurs in α₄ (∂α₄/∂ψ′) from about 30 to 330°(regions I, II and III) regardless of the value of Δ′. For values of Δ′near 0 and 90°, sensitivity to ψ′ is also evident in β₄ (∂β₄/∂ψ′). Themaximum sensitivity to ψ′ occurs in β² (∂β₂/∂ψ′) in regions I and III,and in α₄ (∂α₄/∂ψ′) in region II. Some sensitivity to ψ′ is also seen inβ₄ (∂β₄/∂ψ′) in regions I and III. For Δ′, maximum sensitivity appearsin β₂ (∂β₂/∂Δ′) in regions I and III, and in β₄ (∂β₄/∂Δ′) in region II.Sensitivity to the retardation angle δ also occurs (not shown) such thatthis system also allows a sample independent measure of compensatorretardation. Therefore, ellipsometric operation using a wavelength rangethat induces a range of retardations having retardation values in bothregion II and in at least one of region I and III provides superiorellipsometric information about the sample being probe as compared tothe prior art devices mentioned above.

[0049] We now need to establish the connection between the above resultsand properties of the sample. As described earlier, in an ellipsometricmeasurement a beam of (usually) linearly polarized light is incident onthe surface at non-normal incidence. Reflection is described bymultiplying the p- and s-polarized components, which we can write asEcosP and EsinP, by the complex reflectances r_(p) and r_(s),respectively. Here, P is the azimuth angle of the incident polarizationmeasured with respect to the plane of incidence, and r_(p) and r_(s) arethe complex reflectances for the electric field linearly polarized in,and perpendicular to, the plane of incidence, respectively. Since|r_(p)| is typically less than |r_(s)|, P is usually chosen to besomewhat less than 45° to better approximate the condition ψ′=45° usedin the preceding paragraph. Thus, the field components incident on thepolarization-state detector discussed above are

E _(x) =Er _(p) cos P;  (5a)

E _(y) =Er _(s) sin P.  (5b)

Therefore,

E _(y) /E _(x)=tan ψ′e ^(iΔ′)=tan P tan ψe ^(iΔ),  (5c)

[0050] where ψ and Δ are the conventional angles used to describe thecomplex reflectance ratio ρ=r_(p)/r_(s). Note that for thisconfiguration, Δ=Δ′.

[0051] For thin oxides on a semiconductor substrate, the connectionbetween ρ and the oxide thickness d can be written to first order in d/λas $\begin{matrix}{{\rho \approx {\rho_{o} + {\frac{4\pi \quad {idn}_{a}\cos \quad \theta}{\lambda}\frac{{\varepsilon_{s}\left( {\varepsilon_{s} - \varepsilon_{o}} \right)}\left( {\varepsilon_{o} - \varepsilon_{a}} \right)}{{\varepsilon_{o}\left( {\varepsilon_{s} - \varepsilon_{a}} \right)}\left( {{\varepsilon_{s}\cot^{2}\theta} - \varepsilon_{a}} \right)}}}},} & (6)\end{matrix}$

[0052] where ρ_(o) is the value of ρ for the film-free sample, ε_(s),ε_(o), and ε_(a)=n_(a) ² are the dielectric functions of the substrate,oxide, and ambient, respectively, θ is the angle of incidence, and λ isthe wavelength of light. If |ε_(s)|>>|ε_(o)|>>|ε_(a)| and | ε_(s)cot²θ|>>ε_(a), the above expression reduces to a particularly simpleform:

ρ=ρ_(o)+4πidn_(a) sin θ tan θ/λ,  (7)

[0053] giving d in terms of the data and a set of fundamental constantsindependent of the detailed properties of either substrate or oxide.

[0054] These equations or their exact analogs are solved by the computerprocessor to provide the thickness information of the sample.

[0055] It should be noted that the above embodiment is also ideal foruse as a broadband polarimeter, which is an instrument that measures theoverall reflectance of the sample in addition to the change inpolarization state resulting from such reflectance. This reflectancemeasurement corresponds to the dc component (the first term) in equation(1). Accurately measuring overall reflectance would ideally includedirectly measuring the intensity of the light source with a separatedetector, and using the output from that detector as a normalizingsignal for comparison to the measured amplitude of the reflected light.Broadband polarimetric measurements over a wide range of wavelengths, asa function of wavelength, yield additional information about the sample.

[0056]FIG. 4 illustrates a second embodiment of the present invention,which allows for simultaneous spectroscopic measurement at differentwavelengths, as well as at different angles of incidence. Ellipsometricprinciples can be enhanced not only by measuring the resultingpolarization state as a function of wavelength, but also as a functionof the angle of incidence of the beam onto the sample.

[0057] An ellipsometer device that obtains information at multipleangles of incidence simultaneously is discussed in U.S. Pat. No.5,042,951, issued Aug. 27, 1991 to Gold et al., which is commonly ownedby the present assignee, and is hereby incorporated by reference. Asdescribed in this patent, this ellipsometer analyzes the change inpolarization state of individual rays within the probe beam as afunction of the radial position of the rays. The radial position of therays in the reflected probe beam is related to the angle of incidence ofthe rays on the sample. Using an array detector, the ellipsometricparameters are determined simultaneously at multiple angles ofincidence.

[0058] The second embodiment of the present invention illustrated inFIG. 4 is a broadband spectroscopic ellipsometer that measures thepolarization state over a broad range of wavelengths of light and fordifferent angles of incidence, simultaneously.

[0059] A broadband light source 50 produces a light beam 52 that iscollimated by lens 54. The beam 52 is then passed through a polarizer56, preferably a linear polarizer oriented at an azimuth angle of 0°relative to the beam splitter 58 to create a known polarization state.

[0060] The polarized beam 52 passes through a beam splitter 58 and amicroscope objective lens 60. Preferably, the beam path as it enters thelens 60 is normal to the surface of the sample 2. Lens 60 preferably hasa high numerical aperture, on the order of 0.90 NA. The high numericalaperture is intended to tightly focus the probe beam 52 onto the surfaceof the sample 2 to create rays with a large spread of angles ofincidence. This spread can be on the order of 70 degrees, with a beamspot size on the order of one micron. Therefore, the angle of incidenceof any given ray of light will vary depending upon its radial positionwithin the beam.

[0061] Based on well known ellipsometric principles the polarizationstate of the rays within the beam will change upon interaction with thesample depending upon wavelength and upon the angle of incidence. Thereflected beam will therefore have a mixed polarization state ascompared with the linear polarization state of the incoming beam. Itshould be noted that if the substrate is transparent, the probe beamcould be analyzed after it has been transmitted through the sample.

[0062] Assuming the substrate is substantially opaque, the probe beamwill be reflected by the sample, pass back up through the lens 60 and beredirected by splitter 58. The beam then passes through a rotatingcompensator 68 for retarding the phase of one of the polarization statesof the-beam relative to the other. The compensator thickness andmaterial are selected to produce the desired range of phase retardationscorresponding to the desired wavelength range used to probe the sample.As previously stated above, the range of phase retardations includesvalues within Region II, and in at least one of Regions I and III, ofFIG. 3, thus providing useful information about the sample's surfacestructure over a broad range of wavelengths.

[0063] The beam then passes through an analyzer 70, preferably a linearpolarizer oriented at an azimuth angle of 0° relative to thepolarization direction of the polarizer 56. The analyzer 70 ispreferably a quartz Rochon or Wollaston prism.

[0064] As noted above, the compensator 68 can be located anywhere alongbeam 52 so long as it is somewhere between polarizer 56 and analyzer 70.

[0065] Beam 52 then enters detector 72, which simultaneously measuresthe intensity of the beam components as a function of wavelength and asa function of the radial position r within the beam. The radial positionr is related to the angle of incidence upon the sample, θ, through theexpression r=d sin θ, where d is the focal length of the objective lens.Processor 73 processes the light intensity information measured bydetector 72 to determine the ellipsometric parameters of the sample,using the equations discussed above for the simultaneous measurement ofthe different wavelengths throughout the broad wavelength range ofinterest, as well as for measurements that depend upon the differentangles of incidence.

[0066] The are several techniques for detecting and measuring thebroadband light transmitted by analyzer 70 as a function of bothwavelength and angle of incidence, simultaneously. These methods are nowdiscussed below.

[0067]FIG. 5 illustrates one embodiment of the detector 72, whichincludes a dispersive element 74 that angularly disperses the beam 14 asa function of wavelength in one axis (i.e. vertically), and angularlydisperses the beam 14 as a function of radial position in an orthogonalaxis (i.e. horizontally). A two dimensional detector array 78 with aplurality of detector elements 80 disposed along both axes (rows andcolumns) simultaneously measures the different intensities of thedispersed beam as a function of wavelength and as a function of theangle of incidence. The dispersive element illustrated in FIG. 5 is acurved grating that disperses the beam according to wavelength in thevertical (Y) axis and according to radial position in the horizontal (X)axis. However, a prism, holographic plate, lens, planar grating, and/ora combination thereof could be used as the dispersive element.

[0068]FIG. 6 illustrates another embodiment of detector 72, whichimproves the spectral separation of the beam in contrast to the detectorembodiment of FIG. 5. U.S. Pat. No. 5,412,473, issued on May 2, 1995 toRosencwaig et al., which is commonly owned by the present assignee, andwhich is hereby incorporated by reference, addresses the problem of datablurring caused by insufficient wavelength isolation. There needs to besignificant isolation for the wavelength and angle of incidencemeasurements to prevent a blurring of the data. One disadvantage of thedetector embodiment of FIG. 5 is that the image of the beam for onewavelength of interest will tend to overlap the image of the beam for aslightly different wavelength of interest. The vertical dispersion ofthe beam induced by the dispersive element can be insufficient to fullyseparate the beam images for the different wavelengths of interest. Theresulting overlapping beam images on the photo detector array blurs thewavelength data with the angle of incidence data.

[0069] Therefore, the alternate embodiment of the detector 72illustrated in FIG. 6 addresses the above mentioned problem of datablurring. A relay lens 90 focuses a magnified image of the sample'ssurface down onto a plate 92 having an aperture 94 that is dimensionedto only transmit a portion of the relayed sample image. By adjusting themagnification provided by relay lens 90 as well as the size of theaperture 94, the size of the field of the sample which is eventuallyimaged on detector array 102 can be accurately controlled.

[0070] The beam exiting aperture 94 then passes through aperture 98 offilter 96, which is configured to transmit only a portion of thereflected beam. In the preferred embodiment, aperture 98 is in the formof an elongated slit and is positioned at the relay image plane of theobjective lens 60. The length of aperture 98 is oriented perpendicularto the direction which a dispersion element 100 angularly spreads thelight as a function of wavelength. Preferably, the dimensions of theaperture 98 are selected so that the image transmitted to detector array102 will be on the order of the dimensions of a single row of detectorelements 104.

[0071] The resulting beam impinging upon the photodetector array 102contains a series of segments that are horizontally dispersed as afunction of the angle of incidence upon the sample, and are verticallydispersed as a function of wavelength. Two such segments 106 and 107representing two different wavelengths of interest are illustrated inFIG. 7, where the full images of the two wavelengths are shown inphantom. Each segment 106/107 includes all the angle of incidenceinformation corresponding to that wavelength along the length thereof.Had the full beam images of the two wavelengths been directed to thearray 102, the partially overlapping images would have blurred togetherthe wavelength and the angle of incidence data. However, with thedetector illustrated in FIG. 6, there is no blurring of wavelengthinformation with angle of incidence information for wavelengths havingany significant difference.

[0072] A third embodiment of the present invention is illustrated inFIG. 8. This embodiment is an apparatus for simultaneously generating anintegrated ellipsometric signal, but over a broader range of wavelengthsthan previously thought possible.

[0073] The angle integrated ellipsometer of FIG. 8 increases themeasured signal and thus increases the signal to noise ratio over abroad range of wavelengths. This integrated ellipsometer approach isdescribed in U.S. application Ser. No. 08/327,315, filed on Oct. 21,1994 by Jeffrey T. Fanton et al. The application is commonly owned bythe present assignee and is hereby incorporated by reference.

[0074] This third embodiment of the present invention is the same as thesecond embodiment, except for detector 72. As illustrated in FIG. 8,detector 72 of this third embodiment includes lens 110 that focuses thebeam 52 onto filter 112 that preferably transmits light through twoopposed quadrants 114 and 116 while blocking light striking quadrants118 and 120. The beam transmitted through filter 112 is focused by lens122 through aperture 124 of spatial filter 126.

[0075] After passing through the spatial filter 126, the light beam isboth focused and angularly dispersed as a function of wavelength. Thedispersing element 128 is preferably a curved grating as shown in FIG.8. However, these two functions could be performed by two separateoptical elements (i.e. a curved mirror or lens and a separate planargrating or prism). The step of focusing the light functions to combineall of the various angle of incidence information from the transmittedbeam in order to create an angle integrated output. The grating 78 alsofunctions to angularly disperse the light as a function of wavelength inorder to isolate the wavelength information.

[0076] The focused and angularly dispersed light is directed to a linearphotodetector array 130 that includes a plurality of individual detectorelements 132. Each element receives and measures the intensity of lightover a narrow wavelength region. Processor 134 processes the measuredintensities of light for each of the detector elements 132 to determinethe ellipsometric properties of sample 2.

[0077] It should be understood that the detector arrangement shown inFIG. 8, including the spatial filter 126, grating 128 and photodetectorarray 130 is similar to the components used in a conventionalspectrophotometer. There are therefore a number of other optical layoutswhich are available to perform the focusing and dispersing functions ofthe subject invention. It should also be understood, however, that aconventional spectrophotometer does not include the other elements ofFIG. 8, including the optical elements for generating the ellipsometricsignal of interest and the filter 112 for isolating that signal.

[0078] It is to be understood that the present invention is not limitedto the embodiments described above and illustrated herein, butencompasses any and all variations falling within the scope of theappended claims. For example, as stated above, broadband spectralellipsometric operation at a particular retardation value, i.e. X°, iseffectively equivalent to operation at retardation values at multiplesof 360°, i.e. X°±n360°, where n is any integer. Similarly, phaseretardation ranges, such as X° to Y°, are effectively equivalent tooperation at any range X°+n360° to Y°+n360°. Therefore, any actual phaseretardation value (or range of values) is effectively equivalent to thecorresponding “effective” retardation values (and effective ranges ofvalues), which are the plus or minus 360° multiples thereof.Alternately, any “effective” retardation value encompasses and isequivalent to the actual retardation value and any plus or minus 360°multiples thereof.

What is claimed is:
 1. A broadband spectroscopic ellipsometer forevaluating a sample comprising: a light generator that generates a beamof polychromatic light having a range of wavelengths and a knownpolarization for interacting with the sample; a compensator disposed inthe path of the light beam to induce phase retardations of apolarization state of the light beam wherein the range of wavelengthsand the compensator are selected such that at least a first effectivephase retardation value is induced that is within a primary range ofeffective retardations of substantially 135° to 225°, and at least asecond effective phase retardation value is induced that is outside ofsaid primary range; said compensator being rotatable about an axissubstantially parallel to the propagation direction of the light beam;an analyzer that interacts with the light beam after the light beaminteracts with the sample; and a detector that measures the intensity ofthe light after the interaction with the analyzer as a function ofwavelength and of a rotation angle of the compensator about said axis,including light intensities of those wavelengths corresponding to saidfirst and second effective phase retardation values, wherein saidintensities correspond to the polarization state of the light impingingon the analyzer.
 2. The broadband spectroscopic ellipsometer of claim 1,wherein the first effective phase retardation is defined as either anactual phase retardation within the range of 135° to 225° or a 360°multiple thereof, where the 360° multiple is defined as a range of(135°+n360°) to (225°+n360°) where n is any integer.
 3. The broadbandspectroscopic ellipsometer of claim 1, further comprising: a processorthat determines the polarization state of the light, after theinteraction with the analyzer, from the intensities measured by thedetector.
 4. The broadband spectroscopic ellipsometer of claim 3,wherein said detector measures the intensities of the wavelengths insaid range of wavelengths simultaneously.
 5. The broadband spectroscopicellipsometer of claim 4, wherein. said light generator comprises: alight source that generates a beam of polychromatic light; and apolarizer that polarizes the light beam before the light beam interactswith the sample.
 6. The broadband spectroscopic ellipsometer of claim 4,wherein the range of wavelengths and the compensator are selected toinduce a range of effective phase retardations that exceeds 180°.
 7. Thebroadband spectroscopic ellipsometer of claim 4, wherein the range ofwavelengths and the compensator are selected to induce a range ofeffective phase retardations that is substantially centered around aneffective phase retardation value of 180°.
 8. The broadbandspectroscopic ellipsometer of claim 4, wherein the polarizer and theanalyzer are linear polarizers.
 9. The broadband spectroscopicellipsometer of claim 4, wherein the detector comprises: a dispersingelement that angularly disperses the beam after interacting with theanalyzer as a function of wavelength to a photo detector array.
 10. Thebroadband spectroscopic ellipsometer of claim 9, wherein the dispersingelement is one of a diffraction grating, a holographic plate and aprism.
 11. The broadband spectroscopic ellipsometer of claim 10, whereinthe compensator comprises: a pair of plates of optically anisotropicmaterial having fast axes that are orthogonal to each other.
 12. Thebroadband spectroscopic ellipsometer of claim 11, wherein theanisotropic material is optically active and said pair of plates havehandednesses that are opposite to each other.
 13. The broadbandspectroscopic ellipsometer of claim 3, further comprising: a lens thatfocuses the beam onto the sample to create a spread of angles ofincidence, wherein the detector measures intensities of light after theinteraction with the analyzer both as a function of wavelength and as afunction of angle of incidence.
 14. The broadband spectroscopicellipsometer of claim 13, wherein said detector measures the intensitiesof the wavelengths in said range of wavelengths simultaneously.
 15. Thebroadband spectroscopic ellipsometer of claim 14, wherein the range ofwavelengths and the compensator are selected to induce a range ofeffective phase retardations that exceeds 180°.
 16. The broadbandspectroscopic ellipsometer of claim 14, wherein the range of wavelengthsand the compensator are selected to induce a range of effective phaseretardations that is substantially centered around an effective phaseretardation value of 180°.
 17. The broadband spectroscopic ellipsometerof claim 14, wherein the polarizer and the analyzer are linearpolarizers.
 18. The broadband spectroscopic ellipsometer of claim 14,wherein the detector includes: dispersing element that angularlydisperses the beam transmitted by the analyzer as a function ofwavelength in one axis, and as a function of radial position within thebeam in an orthogonal axis to the one axis to a two-dimensional photodetector array.
 19. The broadband spectroscopic ellipsometer of claim18, wherein the dispersing element includes at least one of a planardiffraction grating, a curved diffraction grating, a holographic plate,a prism, and a lens.
 20. The broadband spectroscopic ellipsometer ofclaim 19, wherein the detector further includes a filter having a shapedaperture that passes only a portion of the beam to the dispersingelement.
 21. The broadband spectroscopic ellipsometer of claim 14,wherein the compensator comprises: a pair of plates of opticallyanisotropic material having fast axes that are orthogonal to each other.22. The broadband spectroscopic ellipsometer of claim 21, wherein theanisotropic material is optically active and said pair of plates havehandednesses that are opposite to each other.
 23. The broadbandspectroscopic ellipsometer of claim 3, further comprising: a lens thatfocuses the beam onto the sample to create a spread of angles ofincidence; and a filter that transmits at least a portion of the beampassing through a pair of opposed radial quadrants and blocks at least aportion of the beam passing through the remaining pair of radialquadrants disposed orthogonally thereto.
 24. The broadband spectroscopicellipsometer of claim 23, wherein said detector measures the intensitiesof the wavelengths in said range of wavelengths simultaneously.
 25. Thebroadband spectroscopic ellipsometer of claim 24, wherein the range ofwavelengths and the compensator are selected to induce a range ofeffective phase retardations that exceeds 180°.
 26. The broadbandspectroscopic ellipsometer of claim 24, wherein the range of wavelengthsand the compensator are selected to induce a range of effective phaseretardations that is substantially centered around an effective phaseretardation value of 180°.
 27. The broadband spectroscopic ellipsometerof claim 24, wherein the polarizer and the analyzer are linearpolarizers.
 28. The broadband spectroscopic ellipsometer of claim 24,wherein: the detector includes a dispersing element that angularlydisperses the beam transmitted by the analyzer as a function ofwavelength.
 29. The broadband spectroscopic ellipsometer of claim 28,wherein the dispersing element includes at least one of a planardiffraction grating, a curved diffraction grating, a holographic plate,a prism, and a lens.
 30. The broadband spectroscopic ellipsometer ofclaim 29, wherein the compensator comprises: a pair of plates ofoptically anisotropic material having fast axes that are orthogonal toeach other.
 31. The broadband spectroscopic ellipsometer of claim 30,wherein the anisotropic material is optically active and said pair ofplates have handednesses that are opposite to each other.
 32. A methodof analyzing a sample comprising the steps of: generating a beam ofpolychromatic light having a range of wavelengths and a knownpolarization for interacting with the sample; inducing phaseretardations of a polarization state of the light beam with acompensator by selecting the range of wavelengths and the compensatorsuch that at least a first effective phase retardation value is inducedthat is within a primary range of effective phase retardations ofsubstantially 135° to 225°, and at least a second effective phaseretardation value is induced that is outside of said primary range;rotating the compensator about an axis substantially parallel to thepropagation direction of the light beam; subjecting the light beam tointeraction with an analyzer after the beam interacts with the sample;measuring the intensity of the light after interaction with the analyzeras a function of wavelength and of a rotation angle of the compensatorabout said axis, including light intensities of those wavelengthscorresponding to said first and second effective phase retardationvalues, wherein said intensities correspond to the polarization state ofthe light impinging on the analyzer.
 33. The method of claim 32 whereinthe first effective phase retardation is defined as either an actualphase retardation in the range of 135° to 225° or a 360° multiplethereof, where the 360° multiple is defined as a range of (135°+n360°)to (225°+n360°) where n is any integer.
 34. The method of claim 32further comprising the step of: processing the measured lightintensities to determine the polarization state of the light after theinteraction with the analyzer.
 35. The method of claim 34 wherein themeasuring step includes measuring the wavelengths in said range ofwavelengths simultaneously.
 36. The method of claim 35 wherein thegenerating step includes: generating a beam of polychromatic light; andpolarizing the light beam before the light beam interacts with thesample.
 37. The method of claim 35 wherein the selecting step furtherincludes selecting the range of wavelengths and the compensator toinduce a range of effective phase retardations that exceeds 180°. 38.The method of claim 35 wherein the selecting step further includesselecting the range of wavelengths and the compensator to induce a rangeof effective phase retardations that is substantially centered around aneffective phase retardation value of 180°.
 39. The method of claim 35wherein the polarizing step and the transmitting step are performedusing linear polarizers.
 40. The method of claim 35 wherein themeasuring step includes the step of: angularly dispersing thetransmitted beam as a function of wavelength to an array of photodetector elements.
 41. The method of claim 40 wherein the dispersingstep includes using a dispersing element that is at least one of aplanar diffraction grating, a curved diffraction grating, a holographicplate, a prism, and a lens.
 42. The method of claim 34 furthercomprising the steps of: focusing the beam onto the sample to create aspread of angles of incidence; collimating light reflected by thesample; and the measuring step comprising measuring the intensities ofthe light transmitted by the analyzer both as a function of wavelengthand as a function of angle of incidence.
 43. The method of claim 42wherein the measuring step includes measuring the wavelengths in saidrange of wavelengths simultaneously.
 44. The method of claim 43 whereinthe selecting step further includes selecting the range of wavelengthsand the compensator to induce a range of effective phase retardationsthat exceeds 180°.
 45. The method of claim 43 wherein the selecting stepfurther includes selecting the range of wavelengths and the compensatorto induce a range of effective phase retardations that is substantiallycentered around an effective phase retardation value of 180°.
 46. Themethod of claim 43 wherein the polarizing step and the transmitting stepare performed using linear polarizers.
 47. The method of claim 43wherein the measuring steps include the step of: angularly dispersingthe transmitted beam as a function of wavelength in one axis, and as afunction of radial position within the beam in an orthogonal axis, to atwo dimensional array of photo detector elements.
 48. The method ofclaim 47 wherein the dispersing step includes using at least one of aplanar diffraction grating, a curved diffraction grating, a holographicplate, a prism, and a lens.
 49. The method of claim 43 wherein themeasuring step includes placing a filter into the beam having a shapedaperture that passes only a portion of the beam before the angularlydispersing step.
 50. The method of claim 34 further comprising the stepsof: focusing the beam onto the sample to create a spread of angles ofincidence; collimating light reflected by the sample; and filtering thebeam after interacting with the sample with a quad filter that transmitsat least a portion of the beam passing through a pair of opposed radialquadrants and blocks at least a portion of the beam passing through theremaining pair of radial quadrants disposed orthogonally thereto. 51.The method of claim 50 wherein the measuring step includes measuring thewavelengths in said range of wavelengths simultaneously.
 52. The methodof claim 51 wherein the selecting step further includes selecting therange of wavelengths and the compensator to induce a range of effectivephase retardations that exceeds 180°.
 53. The method of claim 51 whereinthe selecting step further includes selecting the range of wavelengthsand the compensator to induce a range of effective phase retardationsthat is substantially centered around a phase retardation value of 180°.54. The method of claim 51 wherein the polarizing step and thetransmitting step are performed using linear polarizers.
 55. The methodof claim 51 wherein the measuring steps include the step of: angularlydispersing the transmitted beam as a function of wavelength to an arrayof photo detector elements.
 56. The method of claim 55 wherein thedispersing step includes using at least one of a planar diffractiongrating, a curved diffraction grating, a holographic plate, a prism, anda lens.